Aircraft: EMB ERJ 145 ER/LR
Phase of flight: Parked
Anomaly: Aircraft Equipment Problem Less Severe; Deviation / Discrepancy - Procedural Published Material / Policy

Upon reviewing the aircraft logbooks; I saw that the yaw trim switch on the First Officer's yoke had been MEL'd. Per the MEL; the yaw trim can only be MEL'd on the Non-Flying Pilot's side; which we interpreted to mean that the PIC would have to fly all day. Continuing with the setup check; we found that the auto pilot would not engage regardless of which side it was coupled to; however; the yaw damper was still engaging. I then wrote up the autopilot and called Maintenance. Discussing the issue with them; we troubleshot the issue and were still unable to get the autopilot to engage. When Maintenance arrived; we again tried several ways to troubleshoot the issue which included discussing the yaw trim switch and that the yaw trim switch on the First Officer's side should have been deactivated. They then had me do a complete electrical reset. Upon restarting the aircraft; instead of the aircraft enunciating 'aural unit ok' the aircraft announced 'trim.' Speaking with the mechanics; they said that was weird; but probably because the trim was deactivated and they were considering MEL'ing the autopilot. I called Dispatch to discuss with them if the autopilot was MEL'd in conjunction with the MEL restricting control to the Captain's side; we felt comfortable doing a turn but taking into account our schedule; the weather; and the nature of the MELs; we would like a new aircraft when we returned. I was told we had 6 broken aircraft with no spares and it would not be possible to get a new aircraft upon returning. I then brought up that I would not be comfortable being restricted to the PIC alone required to hand flying the aircraft into and out of bad/low weather with snow and icing for the 5 legs on the long day we were assigned that day. I was then told if I am refusing the aircraft that I had to make contact with the Chief Pilot on call to discuss the issue. Reaching out to [the Chief Pilot] and speaking about the issue; we tried several more techniques for troubleshooting and thinking through the issue from a pilot's perspective. At one point during the troubleshooting; we got the autopilot fail message with yaw damper fail displayed on the EICAS. We tried some other techniques which included pulling the circuit breaker; (all under the supervision of maintenance) for the First Officer trim switch. This led to a master warning that the system logic disabled the entire trim system. We came to the conclusion that with the aircraft enunciating 'trim' on startup instead of 'aural unit ok' and the master warning and deactivation of the entire trim system when it shouldn't have been deactivated through that 1 CB; that there was more going on with the trim system and that it hadn't been fully deactivated as Maintenance had said. In completing the phone call; we had agreed that the aircraft was unsafe to fly in the current condition due to the likelihood that something bigger was going on in the entire trim system and that it effectively hadn't been deactivated entirely and that may be what was affecting the autopilot. EMB First Officer reported refusing an aircraft that exhibited yaw trim and autopilot issues during preflight checks.